Dispersive response of atoms trapped near the surface of an optical nanofiber with applications to quantum nondemolition measurement and spin squeezing
Xiaodong Qi, Ben Q. Baragiola, Poul Jessen, Ivan Deutsch
We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first-principles stochastic master equation to model the squeezing as a function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of $\ensuremath{\sim}5$ dB is achievable with current technology for $\ensuremath{\sim}2500$ atoms trapped 180 nm from the surface of a nanofiber with radius $a=225$ nm.
We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first-principles stochastic master equation to model the squeezing as a function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of \ensuremath∼5 dB is achievable with current technology for \ensuremath∼2500 atoms trapped 180 nm from the surface of a nanofiber with radius a=225 nm.
We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first principles stochastic master equation to model the squeezing as function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of ~5 dB is achievable with current technology for ~2500 atoms trapped 180 nm from the surface of a nanofiber with radius a=225 nm.
We study the enhancement of cooperativity in the atom-light interface near a nanophotonic waveguide for application to quantum nondemolition (QND) measurement of atomic spins. Here the cooperativity per atom is determined by the ratio between the measurement strength and the decoherence rate. Counterintuitively, we find that by placing the atoms at an azimuthal position where the guided probe mode has the lowest intensity, we increase the cooperativity. This arises because the QND measurement strength depends on the interference between the probe and scattered light guided into an orthogonal polarization mode, while the decoherence rate depends on the local intensity of the probe. Thus, by proper choice of geometry, the ratio of good-to-bad scattering can be strongly enhanced for highly anisotropic modes. We apply this to study spin squeezing resulting from QND measurement of spin projection noise via the Faraday effect in two nanophotonic geometries, a cylindrical nanofiber and a square waveguide. We find that, with about 2500 atoms and using realistic experimental parameters, $\ensuremath{\sim}6.3$ and $\ensuremath{\sim}13$ dB of squeezing can be achieved on the nanofiber and square waveguide, respectively.
New effects can arise in quantum physics when there is strong coupling, either between atoms and light or between different quantum systems. This thesis examines an optical nanofiber atom trap as a mediator of atom-light interactions and a potential element of a hybrid quantum system. The evanescent field around the sub-wavelength waist of an optical nanofiber possesses a small mode area that increases the cooperativity between atoms and the mode, in a manner analogous to traditional cavity QED. We demonstrate trapping of 87Rb atoms with an optical nanofiber, confining hundreds of atoms with typical trap lifetimes of tens of milliseconds. We then employ single photon counting techniques to study untrapped ensembles of cold atoms around the nanofiber. A first experiment uses intensity autocorrelations of resonance fluorescence emitted into the nanofiber mode to observe a transition from classical to nonclassical photon statistics. Measuring the correlations on longer timescales reveals the motion of atoms through the optical mode, and we develop a correspondence between the transit time and atomic cloud temperature. A second experiment measures Purcell enhancement of spontaneous emission of atoms near the nanofiber by correlating their fluorescence with a known trigger event. The spontaneous decay rate of an atom near a dielectric is modified by the induced dipole and by a change in the modes of the vacuum electromagnetic field. Our observed enhancement of 6.5±0.9% over the free-space rate matches well with what one finds from mode simulations in our system.
We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition (QND) measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.
In this thesis, I present the realization of a fiber-optical interface using optically trapped cesium atoms, which is an efficient tool for coupling light and atoms. The basic principle of the presented scheme relies on the trapping of neutral cesium atoms in a two-color evanescent field surrounding a nanofiber. The strong confinement of the fiber guided light, which also protrudes outside the nanofiber, provides strong confinement of the atoms as well as efficient coupling to near-resonant light propagating through the fiber. In chapter 1, the necessary physical and mathematical background describing the propagation of light in an optical fiber is presented. The exact solution of Maxwell’s equations allows us to model fiber-guided light fields which give rise to the trapping potentials and the atom-light coupling in the close vicinity of a nanofiber. Chapter 2 gives the theoretical background of light-atom interaction. A quantum mechanical model of the light-induced shifts of the relevant atomic levels is reviewed, which allows us to quantify the perturbation of the atomic states due to the presence of the trapping light-fields. The experimental realization of the fiber-based atom trap is the focus of chapter 3. Here, I analyze the properties of the fiber-based trap in terms of the confinement of the atoms and the impact of several heating mechanisms. Furthermore, I demonstrate the transportation of the trapped atoms, as a first step towards a deterministic delivery of individual atoms. In chapter 4, I present the successful interfacing of the trapped atomic ensemble and fiber-guided light. Three different approaches are discussed, i.e., those involving the measurement of either near-resonant scattering in absorption or the emission into the guided mode of the nanofiber. In the analysis of the spectroscopic properties of the trapped ensemble we find good agreement with the prediction of theoretical model discussed in chapter 2. In addition, I introduce a non-destructive scheme for the interrogation of the atoms states, which is sensitive to phase shifts of far-detuned fiber-guided light interacting with the trapped atoms. The inherent birefringence in our system, induced by the atoms, changes the state of polarization of the probe light and can be thus detected via a Stokes vector measurement.
Cold atom-nanophotonic systems constitute a powerful research platform for the exploration of new regimes of light-matter interaction. The guided light in nanophotonic systems are tightly confined, and often used to trap and manipulate cold atoms at subwavelength distance away from the surface. While the initialization of atomic internal degrees of freedom in these systems has been achieved, a full control of the atomic quantum state also requires manipulating and preparing the atomic motional state at the quantum level. In this thesis, we explore and characterize the coupling between motional and spin degrees of freedom in nanofiber-trapped atoms. This coupling originates from the strong polarization gradient which occurs naturally in spatially confined light fields, i.e., the guided light field in a nanophotonic system. We demonstrate that the spin-motion coupling can be utilized to implement degenerate Raman cooling and prepare atoms close to the three-dimensional motional ground state.We obtain mean numbers of motional quanta of nanofiber-trapped atoms using heterodyne fluorescence spectroscopy. Building on this work, we then use the spin-motion coupling for nanofiber-trapped atoms to realize a mechanical analogue of the Dicke model. We infer the energy spectrum of the system from transitions observed in the fluorescence spectrum. We show that our system reaches the ultrastrong coupling regime. Moreover, we demonstrate that the coupling strength can be readily tuned using an additional nanofiber-guided light field. Furthermore, we achieve imaging of single nanofiber-trapped atoms. Taking advantage of degenerate Raman cooling, we cool atoms near the motional ground state while collecting atomscattered light using a camera. We show single atoms can be detected by imaging at an integration time far less than the trapping lifetime. To demonstrate the potential of this technique, we perform two proof of principle experiments. First, we measure the extinction of a nanofiberguided light atom by atom, and verify the Beer-Lambert Law in the few atoms regime. Second, we detect the atom-scattered light that is coupled to the nanofiber. We observe interference of scattered light fields as a function of the distance between two trapped atoms. By controlling atomic motional states and imaging single atoms, our work in this thesis adds to the toolbox for manipulating and detecting cold atoms interfaced to nanophotonic systems, and paves the way for realizing the bottom-up approach to explore new regimes of light-matter interaction atom by atom.